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Are there "elementary" resources on Penrose Tilings in relation to noncommutative geometry? It's all a big blur to me. There are two transformations S and T that can grow the tilings and every tilin …

In classical mechanics: If a Lagrangian $\mathcal{L}$ is preserved by an infinitesimal change in the state space variables $q_i \to q_i + \varepsilon K_i(q)$, this leads to only second order change in …

The paper Geometry of the Prytz Planimeter described a mechanical instrument whose configuration space is an $S^1$-bundle with an $SU(1,1)$ action. That paper goes on to study the holonomies of variou …

From what I had read, group characters can be "glued" together in a topological fashion and there is something to this effect in the paper by Dijkgraaf and Witten. TQFT seems to be a topological gener …

A paper on supersymmetry in 3-dimensions uses results on the spectra of elliptic operators on $S^3$: The eigenvalues of the vector Laplacian on divergenceless vector fields is $(\ell + 1)^2$ wit …

In physics papers, the massless free boson has a definition involving an action: $$ S(X) = \frac{1}{8\pi} \int d\sigma^2\, \partial X \overline{\partial X}$$ The random functions $X(z)$ are sample …

The matrix-tree theorem states the number of spanning trees of a graph $G$ is equal to a modified determinant of the adjacency matrix or "graph Laplacian", $\Delta_G$: $$\#\{ \text{spanning trees of } …

Buried in the physics paper by Nekrasov and Okounkov, a strange identity is proven: $$ \prod_{n > 0} (1 - q^n)^{\mu^2-1} = \sum_{\mathbf{k}} q^{|\mathbf{k}|} \prod_{\square \in k} \left( 1 - \frac{\mu …

I am trying to find a correspondence between 6-vertex model and an Aztec Diamond tiling. Here are the building blocks of the 8-vertex model: There seems to be more than one correspondence. I foun …

The answer to my question is "yes". Technically, it's a spin-TQFT but now I am trying to make sense of that answer. Dimers on surface graphs and spin structures. I David Cimasoni, Nicolai Resheti …

Is there a link between the theory of Domino Tilings and the Ising Model? In the global qualitative sense that physicists use, the answer is "yes". The connections could go like this: The dimer m …

I was reading about realizations of the "Fibonacci" fusion ring $X \otimes X = X \oplus 1$ in Fusion Categories of Rank 2 by Victor Ostrik. Apparently, there are two of them and they arise in various …

I have read in various places the following objects are related: orthogonal polynomials birth-death processes Lattice paths continued fractions After a lot of searching online, I found sketches ab …

In Terence Tao's discussion of the Gaussian Unitary Ensemble, he derives the Dyson and Airy kernels. The GUE is the probability distribution of the eigenvalues of a random Hermitian matrix. \[ \int …

I am trying to understand better the quantization of the harmonic oscillator. Here are three ways of thinking about the harmonic oscillator. Eigenfunctions of the differential operator: $H = -\frac{ …